Expressions and Equations 6th Grade - Free Printable

Let's solve each of the quadratic expressions by combining like terms. Like terms are terms that have the same variable raised to the same power.

We will go through each expression one by one:

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1. $-3q^2 + 6 - 5q^2 - 9q + 8$

Group like terms:
- $-3q^2 - 5q^2 = -8q^2$
- $-9q$ (only one $q$ term)
- $6 + 8 = 14$

✔ Answer: $-8q^2 - 9q + 14$

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2. $6k^2 - 4 + 7k^2 + 1 - 5k$

Group like terms:
- $6k^2 + 7k^2 = 13k^2$
- $-5k$ (only one $k$ term)
- $-4 + 1 = -3$

✔ Answer: $13k^2 - 5k - 3$

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3. $4 + 7p^2 - 3p^2 + 5n + n$

Group like terms:
- $7p^2 - 3p^2 = 4p^2$
- $5n + n = 6n$
- $+4$ (constant)

✔ Answer: $4p^2 + 6n + 4$

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4. $-9d + 3 + 7d^2 - 3 - 9d$

Group like terms:
- $7d^2$ (only one $d^2$ term)
- $-9d - 9d = -18d$
- $3 - 3 = 0$

✔ Answer: $7d^2 - 18d$

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5. $6 + 9b - 6b^2 + 5b^2 + 8b^2$

Group like terms:
- $-6b^2 + 5b^2 + 8b^2 = (-6 + 5 + 8)b^2 = 7b^2$
- $9b$ (only one $b$ term)
- $+6$ (constant)

✔ Answer: $7b^2 + 9b + 6$

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6. $3bp^2 - 9pq^2 - 2bp^2 - 2 - 5pq$

Note: These terms involve different variables and combinations, so we look for identical variable parts.

- $3bp^2 - 2bp^2 = bp^2$
- $-9pq^2$ (no other $pq^2$ terms)
- $-5pq$ (no other $pq$ terms)
- $-2$ (constant)

✔ Answer: $bp^2 - 9pq^2 - 5pq - 2$

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7. $1 - 6 + 4 + 4 - 7f^2$

Group constants and $f^2$:
- $1 - 6 + 4 + 4 = 3$
- $-7f^2$

✔ Answer: $-7f^2 + 3$

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8. $2s^2 - 4s^2 + 4s - 8s^2 - 7s^2$

Group like terms:
- $2s^2 - 4s^2 - 8s^2 - 7s^2 = (2 - 4 - 8 - 7)s^2 = -17s^2$
- $+4s$ (only one $s$ term)

✔ Answer: $-17s^2 + 4s$

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9. $5a^2 + 6a^2 + 4 - 5a^2 + 2a^2$

Group like terms:
- $5a^2 + 6a^2 - 5a^2 + 2a^2 = (5 + 6 - 5 + 2)a^2 = 8a^2$
- $+4$ (constant)

✔ Answer: $8a^2 + 4$

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10. $-8 + 7 - 3q^2 - 3q + 5q^2$

Group like terms:
- $-3q^2 + 5q^2 = 2q^2$
- $-3q$ (only one $q$ term)
- $-8 + 7 = -1$

✔ Answer: $2q^2 - 3q - 1$

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✔ Final Answers:

1. $-8q^2 - 9q + 14$
2. $13k^2 - 5k - 3$
3. $4p^2 + 6n + 4$
4. $7d^2 - 18d$
5. $7b^2 + 9b + 6$
6. $bp^2 - 9pq^2 - 5pq - 2$
7. $-7f^2 + 3$
8. $-17s^2 + 4s$
9. $8a^2 + 4$
10. $2q^2 - 3q - 1$

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📌 Summary of Steps:

- Identify like terms (same variables and exponents).
- Combine coefficients.
- Write simplified expression in standard form (descending powers).

Let me know if you'd like these written out in a formatted worksheet or need help with graphing or factoring next!